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A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is there a substantial difference? Human activity Natural patterns Don't know Male 331 46 162 179 Female 317 45 Click here to view the chi-square distribution table. Identify the null and alternative hypotheses. Ho: and are H₁: and are Compute the test statistic. (Round to three decimal places as needed.) Find the critical value(s). (Round to three decimal places as needed. Use a comma to separate answers as needed.) What is the conclusion based on the hypothesis test? Ho. There ▼sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. Men and women to agree.

A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is there a substantial difference? Human activity Natural patterns Don't know Male 331 46 162 179 Female 317 45 Click here to view the chi-square distribution table. Identify the null and alternative hypotheses. Ho: and are H₁: and are Compute the test statistic. (Round to three decimal places as needed.) Find the critical value(s). (Round to three decimal places as needed. Use a comma to separate answers as needed.) What is the conclusion based on the hypothesis test? Ho. There ▼sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. Men and women to agree.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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### Investigating Opinions about Global Warming #### Overview A poll was conducted to investigate opinions about global warming. Specifically, respondents who answered "yes" when asked if there is solid evidence that the Earth is getting warmer were subsequently asked to select a cause of global warming. The choices given were: 1. Human activity 2. Natural patterns 3. Don't know The data collected from this poll is summarized in the table below, which considers the respondents' sex in relation to their choice: | | Human Activity | Natural Patterns | Don't Know | |---------------|----------------|------------------|------------| | **Male** | 331 | 162 | 46 | | **Female** | 317 | 179 | 45 | To test if the sex of the respondent is independent of their choice regarding the cause of global warming, we use a significance level of 0.01. #### Hypothesis Testing **Identify the Null and Alternative Hypotheses:** - \(H_0\) (Null Hypothesis): The sex of the respondent is independent of their choice for the cause of global warming. - \(H_1\) (Alternative Hypothesis): The sex of the respondent is not independent of their choice for the cause of global warming. **Compute the Test Statistic:** - Round to three decimal places as needed. **Find the Critical Value(s):** - Round to three decimal places as needed and use a comma to separate the values if more than one value is required. #### Conclusion Based on Hypothesis Test: Based on the computed test statistic and the critical values determined from the chi-square distribution table (using degrees of freedom and significance level), the conclusion can be determined as follows: - Reject \(H_0\): There is sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. - Fail to Reject \(H_0\): There is insufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. #### Chi-Square Distribution Table Below is a partial chi-square distribution table with areas to the right of the critical values and corresponding degrees of freedom: | Degrees of Freedom | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 |
Transcribed Image Text:### Investigating Opinions about Global Warming #### Overview A poll was conducted to investigate opinions about global warming. Specifically, respondents who answered "yes" when asked if there is solid evidence that the Earth is getting warmer were subsequently asked to select a cause of global warming. The choices given were: 1. Human activity 2. Natural patterns 3. Don't know The data collected from this poll is summarized in the table below, which considers the respondents' sex in relation to their choice: | | Human Activity | Natural Patterns | Don't Know | |---------------|----------------|------------------|------------| | **Male** | 331 | 162 | 46 | | **Female** | 317 | 179 | 45 | To test if the sex of the respondent is independent of their choice regarding the cause of global warming, we use a significance level of 0.01. #### Hypothesis Testing **Identify the Null and Alternative Hypotheses:** - \(H_0\) (Null Hypothesis): The sex of the respondent is independent of their choice for the cause of global warming. - \(H_1\) (Alternative Hypothesis): The sex of the respondent is not independent of their choice for the cause of global warming. **Compute the Test Statistic:** - Round to three decimal places as needed. **Find the Critical Value(s):** - Round to three decimal places as needed and use a comma to separate the values if more than one value is required. #### Conclusion Based on Hypothesis Test: Based on the computed test statistic and the critical values determined from the chi-square distribution table (using degrees of freedom and significance level), the conclusion can be determined as follows: - Reject \(H_0\): There is sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. - Fail to Reject \(H_0\): There is insufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. #### Chi-Square Distribution Table Below is a partial chi-square distribution table with areas to the right of the critical values and corresponding degrees of freedom: | Degrees of Freedom | 0.995 | 0.99 | 0.975 | 0.95 | 0.90 | 0.10 |
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